Computational tools have been used in interpreting electrophysiological data and in discovering electrophysiological phenomena for well more than a century. One of the earliest uses of a computational tool in electrophysiology was the application of Lord Kelvin's mathematical model for the propagation of electrical signals through undersea telegraph cables (cable theory) to the problem of conduction of action potentials along nerve and muscle fibers. See Hermann (1905).
Over the years, cable theory has been extended to structures much more complex than simple fibers, so that today it is used in the study of such diverse physiological phenomena as the electrical potentials produced by populations of neurons, the role of dendritic spines in information processing, and the generation of action potentials from synaptic input on branched dendritic trees. See Koch and Segev (1998). Indeed, a number of professional computer programs are now available which allow experimental researchers to use cable theory and, for example, the Hodgkin-Huxley equations to analyze complex experimental data. See, for example, the NEURON software program available at Yale University and Duke University, which is documented in Carnevale and Hines (2005). See also the neural modeling project, nicknamed the Blue Brain Project, being conducted by IBM and The Ecole Polytechnique Fédérale de Lausanne.
At a phenomenological level substantially below that of cable theory, other computational tools have been developed based on the Poisson-Boltzmann and the Poisson-Nernst-Planck equations. These tools have been applied to problems involving the movement of ions in and around biological membranes. Molecular dynamics analyses directed to the movement of individual ions through pores have also been proposed. See Allen et al. (2001). Recently, the mechanisms underlying the gating of biological pores (channels) has been studied using these types of tools. See Islas and Sigworth (2001).
At a phenomenological level substantially above that of cable theory, computational tools based on volume conductor analyses have been used to calculate in detail the electrical fields surrounding individual nerve fibers as well as those produced by entire organs, such as the heart or brain. For example, extensive engineering efforts have been applied to what has become known as the “reverse problem,” where the goal is to determine electrical sources from measurements, e.g., EEG or EKG measurements, made on a patient's skin.
A common characteristic of the computational tools used to date has been their focus on electrical potentials. In addition to the foregoing, see, for example, U.S. Pat. Nos. 5,355,435, 5,947,899, and 7,174,325. This, of course, is the natural parameter to calculate since in practice what researchers measure are electrical potential differences. However, electrical potentials are not primary variables but are the result of “unseen” charge distributions.
As illustrated by the examples set forth below, using the computer-based computational tools of the present invention, it has been found that the charge distributions associated with biological membranes having regions with different electrical properties (e.g., regions with different conductivities and/or regions with and without non-conservative fields (e.g., fields due to chemical potentials)) are highly complex. The complexity is seen in both the charge distributions' temporal and spatial behavior.
The charge distributions identified by the computer-based computational tools of the invention can be expected to play significant roles in the functioning of biological membranes and systems. As just one example, ligand-gated pores change state in response to the presence of the ligand (typically charged) in the vicinity of the pore.
Using the computer-based computational tools of the present invention, spatial and temporal distributions for charged ligands in the vicinity of a pore can be calculated. By studying these distributions, better understandings can be achieved of the operation of such pores. Voltage-gated pores, as well as electrical synapses, can be similarly studied. In short, wherever charged species play a role in the operation of biological membranes, the computer-based computational tools of the present invention can be used to provide insight into how those species are distributed in space, in time, or in both space and time.
In recent years, the relationship between surface charge distributions and the currents they generate has been the subject of original research in the field of physics education and has served as a central theme of at least some textbooks. See Chabay and Sherwood (2002); Heald (1984); Jackson (1996); Jefimenko (1989); Preyer (2000); and Preyer (2002). Indeed, for more than 25 years, it has been known that local surface charge accumulations are needed for current to turn a corner. See Rosser (1970). Yet, as noted above, in the field of electrophysiology, the focus has been on electrical potentials, not charge distributions. As a consequence many fundamental phenomena have been poorly understood or not understood at all. The present invention is directed to providing computer-based computational tools for addressing this deficit in the existing state of the art.